An Interacting Wasserstein Gradient Flow Strategy to Robust Bayesian Inference
arxiv(2024)
Abstract
Model Updating is frequently used in Structural Health Monitoring to
determine structures' operating conditions and whether maintenance is required.
Data collected by sensors are used to update the values of some initially
unknown physics-based model's parameters. Bayesian Inference techniques for
model updating require the assumption of a prior distribution. This choice of
prior may affect posterior predictions and subsequent decisions on maintenance
requirements, specially under the typical case in engineering applications of
little informative data. Therefore, understanding how the choice of prior may
affect the posterior prediction is of great interest. In this paper, a Robust
Bayesian Inference technique evaluates the optimal and worst-case prior in the
vicinity of a chosen nominal prior, and their corresponding posteriors. This
technique employs an interacting Wasserstein gradient flow formulation. Two
numerical case studies are used to showcase the proposed algorithm: a
double-banana-posterior and a double beam structure. Optimal and worst-case
prior are modelled by specifying an ambiguity set containing any distribution
at a statistical distance to the nominal prior, less or equal to the radius.
Examples show how particles flow from an initial assumed Gaussian distribution
to the optimal worst-case prior distribution that lies inside the defined
ambiguity set, and the resulting particles from the approximation to the
posterior. The resulting posteriors may be used to yield the lower and upper
bounds on subsequent calculations used for decision-making. If the metric used
for decision-making is not sensitive to the resulting posteriors, it may be
assumed that decisions taken are robust to prior uncertainty.
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